zenpundit.com » mathematics

Archive for the ‘mathematics’ Category

Jabhat and IS “caliphate” by the numbers

Saturday, July 12th, 2014

[ by Charles Cameron -- large numbers don't fit well into small skulls, but we do what we can ]
.

Charles Lister tweeted today:

The numbers are, for my humble self, staggering.

And you can’t lose $1.5 billion if you didn’t have $1.5 billion at some point to lose.

**

How about the “caliphate”?

Here’s the Jabhat vs ISIS — now IS, aka the “caliphate” — comparison:

Among other things, ISIS “made off with £256 million in cash and a large amount of gold bullion from Mosul’s central bank during its takeover of the city” as the Telegraph reported. That’s a half billion dollars, give or take.

And now IS is presumably “worth” 2 billion. Give or take.

**

To put those figures in perspective, let’s compare IS today with AQ in 2001:

Business Insider calculated bin Laden‘s ROI at the time of his death at 2,514,000 to 1:

Al-Qaida pulled off the Sept. 11 attacks for approximately $500,000, according to the 9/11 Commission report. By the end of fiscal 2011 the U.S. will have spent $1.3 trillion, or 9% of the national debt, fighting the wars in Afghanistan and Iraq according to the Center for Defense Information. But when it’s all said and done the total cost of the wars will make Bin Laden’s 2,514,000:1 return at the time of his death multiply dramatically. It has been projected by Nobel prize winning economist Joseph Stiglitz and others that the lifetime cost of the Iraq and Afghanistan wars will run to approximately $3 trillion, or over 20% of current federal public debt, when long-term medical care for the wounded and other costs are factored.

**

And here’s the current cost comparison with Iraqi losses:

Okay?

I have to confess my mind is a little bit numb with the numbers at this point.

**

If I had time and talent, I suppose I’d make theis whole thing more comprehensible, at least to people like myself, by treating dollar amounts the way XKCD treats radiation — but I don’t, so here’s my attempt to give a wider overview, sorted in ascending order of magnitude to make it easier for me to notice how $millions become $billions become $trillions.

**

Sources:

  • Lister, leaked audio [edited to add: but see comment #1 below]
  • Lister, Golani admits
  • Guardian, $2bn network
  • Telegraph, ISIS’ half-a-billion-dollar heist
  • Business Insider, Bin Laden’s ROI
  • Exec Summary, 9/11 Commission Report [see under "financing"]
  • BasNews, Iraqi costs
  • CIA, GDP Iraq (2013 est)
  • CIA, GDP Syria (2011 est)
  • CIA, GDP USA (2013 est)
  • Share

    Today’s DoubleQuotes 1: in the wild

    Saturday, May 3rd, 2014

    [ by Charles Cameron -- fascinated to see the uses others make of the juxtapositions I call "DoubleQuotes" ]
    .

    This first one was suggested to me by Scott Shipman as a “match” for my DQ about Von Karman’s mathematics of flow in liquids and Van Gogh’s night sky — and indeed, the two of them make a fine double DoubleQuote.

    **

    The second comes from the “HSM Press Office” twitter feed, the exact nature of which is unknown, but which calls itself the “High Spirit Mission Press” and sports a jihadist “black banner” as its avatar:

    **

    And the third?

    M’friend Bryan Alexander suggested what he called “a Piketty doublequote” in a note to me this morning:

    It may be excessive to accuse senior executives of having their “hands in the till”, but the metaphor is probably more apt than Adam Smith’s metaphor of the market’s “invisible hand”

    **

    Let’s take the two visual “DoubleQuotes in the wild” above, and look at my own equivalents:

    I have to say that I find the respective beauties of the von Karman vortext street diagram (upper panel) and the Van Gogh night sky painting (lower panel) seem perfectly balanced to me, while the fractal generator still has a ways to go before it arrives at the brilliance of Hokusai.

    The fractal-wave comparison, btw, is one that has obviously occurred to more than one person — here’s another version:

    It’s also interesting to me that in both cases — that of Hokusai and that of Van Gogh — the arts appear to have been “ahead of” the sciences.

    **

    As to the second “wild” DQ –

    I’ve used TinEye and Google image-search engines, and haven’t found any other uses of the double image HSM Press Office posted, showing an Imam praying for a deceased US soldier and US aoldiers urinating on the bodies of deal Taliban — so I imagine the pairing of the two images may be KSM Press Office’s own. And it’s funny, because I think the intention is to suggest “we” (ie jihadists) treat “you” (ie US military dead) with appropriate respect, while you show no such respect for deal Taliban.

    The thing is, here’s a caption for the photo of the Imam praying:

    Imam Hashim Raza leads mourners in prayer during a funeral for Mohsin Naqvi at al-Fatima Islamic Center in Colonie, N.Y., Monday, Sept. 22, 2008. Naqvi was a Muslim, a native of Pakistan (he emigrated to the U.S. with his family when he was 8 years old and became a citizen at 16) and a U.S. Army officer. He was killed by a roadside bomb while on patrol in Afghanistan. (AP Photo/Mike Groll)

    So what we’re seeing is an American imam at the funeral of a fellow Muslim — in this case a fellow Muslim who was also American soldier. And BTW those American soldiers urinating on Taliban corpses? They’re not representative of the American military as a whole.

    Knowing this, I’ve made my own DoubleQuote in response to the one above.

    In the upper panel, it shows the New York imam at the funeral of Lt. Mohsin A. Naqvi, whose flag-draped coffin was carried to the service by an Army honor guard from Fort Drum’s 10th Mountain Division.

    In the lower panel, we see US medics — marines, I think [ Army, see correction below] — treating wounded Taliban fighters in Afghanistan.

    Share

    Of butterflies, snowboarders, tornados and avalanches

    Monday, April 7th, 2014

    [ by Charles Cameron -- deeply uncertain as to how often he should be grateful for narrow escapes from troubles he was utterly unaware of ]
    .

    See, the first thing I want to know it: is an oblivious butterfly’s wing-flap roughly equivalent to an oblivious snowboader’s short slide across snow? And the second: is a tornado roughly comparable to an avalanche? I mean, a second’s worth of a living creature’s movement in the one case, and a “natural disaster” of somewhat larger proportions in the other?

    Of course, the avalanche was closer to the snowboarder, who wound up “riding” it to safety, than Brazil is to Texas. Is that a difference that makes a difference?

    The first quote above is from Laura Zuckerman‘s Reuters report, No charges for snowboarder who triggered killer Montana avalanche, posted yesterday, and the second is the title of a celebrated talk given to the American Association for the Advancement of Science by Edward Lorenz on December 29, 1972.

    Although if it had been given just 3 days later (a very mild change in initial conditions) it would have been given not merely on a different day and to a different audience, but in a different month and a different year… and maybe even mentioned first in different editions of Encyclopedia Britannica and the OED!

    **

    Well, see, I am also interested because in the paper with that intriguing title, Lorenz also said:

    You can fill the lower panel with your own conclusion as to the question of the snowboarder: is there one of them helping us avoid an avalanche for very one that sets one going? Does it all cancel out in the long run?

    From Zuckerman’s article again, broadening our scope from one incident in Montana to see the wider picture:

    Almost all U.S. avalanches that affect people strike in the backcountry of the mountainous West and are caused by snowmobilers, skiers and snowboarders who inadvertently trigger them. Avalanches have killed 26 people so far this season, records show.

    How many avalanches have we already missed this year thanks to other snowmobilers, skiers and snowboarders? And have we expressed our gratitude?

    **

    On a somewhat similar tack, I wrote back in 2009:

    A deer crossed perhaps twelve feet ahead of my car on the road from Sedona, Arizona to Cottonwood a year or two back. 60 mph is 88 feet per second. A tenth of a second later and the deer and or I would likely have been dead — one full second later, he or she would have crossed sixty feet behind me and I would have seen nothing, known nothing.

    There are deer constantly crossing our paths sixty feet behind us — and it’s a normal day at the office, it’s one more day like any other: sunny, then partly cloudy, with a ten percent chance of rain.

    Another time, and this was in Southern California, my car skidded out of control on a slick road as I was driving home with son Emlyn (then age 10). We hit the 3′ concrete center divider, jumped it, and flipped over, landing upside down. Emlyn and I climbed out with minor scratches — making sure we could climb out through the squished windows was the main issue. We were unscathed, but the car itself was totalled.

    Had I taken that turn three seconds earlier or later, hitting a slicker or drier patch of road, and angling more or less steeply at the center divider — would we have been, in words made famous by wanted posters long before Schrodinger’s cat pondered them: Dead or Alive

    Who knows?

    **

    I suspect we have no idea how many close shaves and narrow escapes we have over the course of a lifetime — but the Recording Angel might know, and be in a state of perpetual hysterics over our ability to ignore a dozen near-disasters while getting totally discombobulated over a very minor incident that we happen to notice…

    Unless the Recording Angel, too, is subject to Heisenberg‘s uncertainty and Schrodinger’s collapse…

    Share

    Of visionary rings, chariots — and tanks

    Monday, March 17th, 2014

    [ by Charles Cameron -- responding to Steve Engel's comment on my post Purim, or Israel vs Iran redux? ]
    .

    Steve picked up on the image of the Merkabah, Ezekiel‘s visionary chariot as five wheels with wings in his comment today:

    noting their resemblance to the Olympic rings. Such patterns have fascinated artists and symbolic thinkers across the centuries.

    Thus the Abbot Joachim of Fiore portrayed the three “ages” of Father, Son and Holy Spirit as interlinked rings in his celebrated Liber Figurarum:

    Cosimo de Medici, in the Renaissance, used the symbol of three interlocking “Borromean” rings on a medallion:

    and indeed, Botticelli paints Pallas wearing the Medici triple rings in his painting, Pallas and the Centaur:

    Jan Valentin Saether favors the Vesica Piscis formed where two circles overlap as the visionary aperture in the ninth image of his Viloshin Letters:

    And the Olympic rings, as befits a logo heavily associated with advertising, might be the most banal of them all — had it not been redeemed one night by the gracious moon hanging low under London Bridge:

    **

    But let us return to Ezekiel’s angelic wheels, which are related to early Jewish “mysticism of the Chariot” or Merkabah:

    The Merkabah…

    Can we find some echo of those wheels, perhaps, in the roadwheels of the IDF Armored Corps’s Merkava IV tank? Pictured here is the Mark I, from 1979.

    Production of the Mark IV continues…

    Share

    Warren McCulloch’s lifetime koan

    Saturday, March 15th, 2014

    [ by Charles Cameron -- from intuitive leap to confirmation in a celebrated paper by neurophysiologist and cybernetician Warren McCulloch ]
    .

    As I mentioned in my earlier post, Close reading, Synoptic- and Sembl-style, for parallels, patterns, there are times when my HipBone-influenced style of reading suggests the presence of a hidden piece of text that forms the basis for the part that’s readily available — in that case, the Qur’anic passage on which a major speech by Bin Laden was based.

    Something very similar happened the other day, while I was reading the cybernetician Warren McCulloch‘s paper What is a number, that a man may know it, and a man, that he may know a number? thoroughly for the first time.

    McCulloch’s title itself triggered an intuitive leap — call it a HipBone / Sembl move — to the Prologue to St John’s Gospel, familiar to me since my altar-boy childhood as the Last Gospel recited by the priest at the end of Mass.

    I’ll have more to say about St John’s Prologue, and scripture more generally, later in this post, when I’ve told you how my “intuitive leap” was confirmed by further readings, and what that means in terms of intuition and verification.

    **

    I call that move from McCulloch to St John an intuitive leap — but as with all such leaps, it is important to verify that the leap is well-founded at both ends.

    Reading on past the title, then, I found McCulloch’s description of his own background, which is relevcant here:

    I was destined for the ministry. Among my teen-age acquaintances were Henry Sloan Coffin, Harry Emerson Fosdick, H. K. W. Kumm, Hecker – of the Church of All Nations – sundry Episcopalian theologians, and that great Quaker philosopher, Rufus Jones.

    In the fall of 1917, I entered Haverford College with two strings to my bow – facility in Latin and a sure foundation in mathematics. I “honored” in the latter and was seduced by it. That winter Rufus Jones called me in. “Warren,” said he, “what is thee going to be?” And I said, “I don’t know.” “And what is thee going to do?” And again I said, “I have no idea; but there is one question I would like to answer: What is a number, that a man may know it, and a man, that he may know a number?” He smiled and said, “Friend, thee will be busy as long as thee lives.”

    In Zen (Buddhist) parlance, Rufus Jones is telling Warren McCulloch that he has found an authentic koan, a paradox to explore and deepen into, sufficient for a lifetime.

    **

    It’s only a little later in McCulloch’s paper that my intuitive leap is “verified” in McCulloch’s own words:

    This lecture might be called, “In Quest of the Logos” or, more appropriately – perverting St. Bonaventura’s famous title – “An Itinerary to Man.” Its proper preface is that St. Augustine says that it was a pagan philosopher – a Neoplatonist – who wrote, “In the beginning was the Logos, without the Logos was not anything made that was made … So begins our Christian theology.”

    But McCulloch doesn’t stop there, he continues right on from theology into mathematics:

    So begins our Christian theology. It rests on four principles. The first is the eternal verities. Listen to the thunder of that saint, in about A.D. 500: “7 and 3 are 10; 7 and 3 have always been 10; 7 and 3 at no time and in no way have ever been anything but 10; 7 and 3 will always be 10. I said that these indestructible truths of arithmetic are common to all who reason.” An eternal verity, any cornerstone of theology is a statement that is true regardless of the time and place of its utterance. Each he calls an idea in the Mind of God, which we can understand but can never comprehend.

    The idea (“mathematics”) and the thinker (“man”) — McCulloch is working at the interface of “mind and matter” — “word and flesh” — the eternal and the temporal. He’s working at what is these days called the “hard problem of consciousness”.

    St John, too, was working at that interface, and brilliantly so — regardless of what credence you put in his theology of the Incarnation of God in Man, it is a brilliant attempt to join the Hebrew “In the Beginning” of Genesis with the Greek “In the Beginning” of his own writings.

    My own point here is this: that an intuitive leap, once made, needs to be grounded or confirmed by slower, more explicit, rational or experimental means.

    **

    Having made my point, I’d like to add some further notes here, for those interested in scriptural matters…

    Here’s John 1.1-14, the celebrated “Prologue” to St John’s Gospel, in the King James version, worth reading whether you know it or not for the comparison that follows with St Augustine’s stunnning reading of the same text:

    In the beginning was the Word, and the Word was with God, and the Word was God. The same was in the beginning with God. All things were made by him; and without him was not any thing made that was made. In him was life; and the life was the light of men. And the light shineth in darkness; and the darkness comprehended it not.

    There was a man sent from God, whose name was John. The same came for a witness, to bear witness of the Light, that all men through him might believe. He was not that Light, but was sent to bear witness of that Light.

    That was the true Light, which lighteth every man that cometh into the world. He was in the world, and the world was made by him, and the world knew him not. He came unto his own, and his own received him not. But as many as received him, to them gave he power to become the sons of God, even to them that believe on his name: Which were born, not of blood, nor of the will of the flesh, nor of the will of man, but of God.

    And the Word was made flesh, and dwelt among us, and we beheld his glory, the glory as of the only begotten of the Father, full of grace and truth.

    **

    Here is Augustine’s comment, from his Confesssions, book VII:

    Thou procuredst for me, by means of one puffed up with most unnatural pride, certain books of the Platonists, translated from Greek into Latin. And therein I read, not indeed in the very words, but to the very same purpose, enforced by many and divers reasons, that In the beginning was the Word, and the Word was with God, and the Word was God: the Same was in the beginning with God: all things were made by Him, and without Him was nothing made: that which was made by Him is life, and the life was the light of men, and the light shineth in the darkness, and the darkness comprehended it not. And that the soul of man, though it bears witness to the light, yet itself is not that light; but the Word of God, being God, is that true light that lighteth every man that cometh into the world. And that He was in the world, and the world was made by Him, and the world knew Him not. But, that He came unto His own, and His own received Him not; but as many as received Him, to them gave He power to become the sons of God, as many as believed in His name; this I read not there.

    Again I read there, that God the Word was born not of flesh nor of blood, nor of the will of man, nor of the will of the flesh, but of God. But that the Word was made flesh, and dwelt among us, I read not there.

    **

    That quote from St Augustine is a striking one — by way of comparison I would like to offer this no-less fascinating excerpt from the Islamic historiographer Ibn Khaldun‘s Muqaddimah, describing developments in the early church from the death of Christ to the establishment of the canon of scriptures:

    The Apostles divided into different groups. Most of them went to the country of the Romans and made propaganda for the Christian religion. Peter was the greatest of them. He settled in Rome, the seat of the Roman emperors. They 420 then wrote down the Gospel that had been revealed to Jesus, in four recensions according to their different traditions. Matthew wrote his Gospel in Jerusalem in Hebrew. It was translated into Latin by John, the son of Zebedee, one of (the Apostles). (The Apostle) Luke wrote his Gospel in Latin for a Roman dignitary. (The Apostle) John, the son of Zebedee, wrote his Gospel in Rome. Peter wrote his Gospel in Latin and ascribed it to his pupil Mark. These four recensions of the Gospel differ from each other. Not all of it is pure revelation, but (the Gospels) have an admixture of the words of Jesus and of the Apostles. Most of (their contents) consists of sermons and stories. There are very few laws in them.

    The Apostles came together at that time in Rome and laid down the rules of the Christian community. They entrusted them to Clement, a pupil of Peter, noting in them the list of books that are to be accepted and in accordance with which one must act…

    **

    Theology, once the Queen of Sciences and now largely ignored, has been laying fallow for centuries. There are rich findings here for those who choose to dig.

    h/t Derek Robinson.

    Share

    Switch to our mobile site